True or False Derivative Questions

True or False and Why? 1.) If f(x) = g(x) + c, then f'(x) = g'(x) 2.) If y = x/pi, then dx/dy = 1/pi 3.) If f(x) = 1/x^n, then f'(x) = 1/(nx^n-1)

Power Series: Interval of Convergence

Find a power series for the function, centered at c, and determine the interval of convergence: f(x)= 4 / 5-x, c=-2

Power series: Interval of Convergence

Determine a power series, centered at 0, for the function, identify the interval of convergence: h(x)= x / x^2-1 = (1 / 2(1+x)) -(1 / 2(1-x))

Application of antiderivatives

A rocket lifts off the surface of the earth with a constant acceleration of 20 m/sec.sq. How fast will the rocket be going 1 minute later? What I did: a=20 m/sec.sq. v=20t+C m/sec, 1 min. = 60 sec. Initial conditions: v=0 when t=0 At t=0, C=0 Speed = |v|=20(60)+0, or 1200 m/sec. Question: Is this correct, or am I leav ...continues

Evaluation of a Function

A certain rational function f(x) contains quadratic functions in both its numerator and denominator. Aside from that, we also know the folliwing things about f: f has a vertical asymptote at x=5 f has a single x-intercept of x=2 f is removably discontinous at x=1, lim as (x)approaches 1 of f(x)= -1/9 evaluate lim of f( ...continues

Finding Inverse of one-to-one Functions Rules and Example

Determine a set of rules for finding the inverse of a function and find the inverse of: f(x) = (x-2)/(x+2)

Sine Cancellation Laws

Using Cancellation Laws and other methods solve the following problems: 1) arcsin(1) 2) sin(arcsin(1/3))

Functions: L-Hopital's Rule

1) use l'Hopital's rule to show (1+r/k)^kà  e^r , kà  infinity 2) show that y(k)=(1+r/k)^k is an increasing function of k greater or equal to 1 3) let xi and yi are cash flows of two projects for i=0,1,2,….,n such that x0 summation from i=0 to i=n (yi). Let Px(d) and Py(d) deno ...continues

Series: Convergence Interval

Find the convergence interval of the following series. x-x^2/2+x^3/3+...+(-1)^(n-1)/n x^n+...

Integration

Intergrate the follow function f(x)=(1+x^2)/(1+x^4)